Use Laplace transforms to solve the differential equation: y' + y – e-t = 0 where y (0) = 0, y (0) = 0

Q: у" +у%3D0.001t?, У (0) %3D 0, у'(0) %3D 1.5

A:

Q: Solve the linear differential equation using Fourier transform.

A: The objective of this question is to solve the given linear differential equation using the Fourier…

Q: y" +6y' + 4y = 10e ; y(0) = 0, y'(0) = -2 Answer: y = et -e-t +e-* 3

A: We are given the differential equation : y''+6y'+4y=10et Taking Laplace transform both sides, we…

Q: 5. x"(t) + 4x(t) = t + 4; x(0) = 1, x'(0) = 0 %3D

A:

Q: y'' – y" + 4y'- 4y = 10e-t, y(0) = 5, y'(0) = -2, y"(0) = 0 %3D %3D

A: Given differential equation is y'''−y''+4y'−4y=10e−t, y0=5,y'0=−2 and y''0=0 Take Laplace transform…

Q: y" – 2y' + 5y = 8e'sin2t, y(0) = 1, y'(0) = -1 %3D

A:

Q: y"(x) + 9y(x) = 40e* ; y(0) = 5, y'(0) = -2

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: 3 Solve the following equations by Laplace transforms. dx (a) + 3x = e-2t dt given that x = 2 when t…

A:

Q: Transform the differential equation y" - 2y" +8y-y=t into a system of first order equations. 1₁ =…

A:

Q: g(t) = 4e13 (t+1) cos (6π fot)

A:

Q: t3 - 3t2 + 5t – 8

A:

Q: #o5 Selve the simultem Eou) equatis m3 using ん·T. プ=1; (()=onx() ナ? -0;1()=y() dt

A:

Q: Use Laplace transform to find the solution of the differential equation with the initial value.

A: Given: y"-y=t-2, y(2)=3, y'(2)=0

Q: 5 sinh (3t) +4 cosh (3t)

A:

Q: ) 3x - 4x= sin社 ; at t=0,x==

A:

Q: y" – 2y' + 3y = 2t²e3t 3 where y'(0) = y(0) = 0

A:

Q: 8. Solve using Laplace transform: y" + 2y – 3y = 8e¬t + 8 (t – ), y(0) = 3, y' (0) = –5.

A:

Q: d*y dr -y = 8(x – a); dx4

A: Differential equation is an equation that represents the relation between variable and their…

Q: Describe the overall process of solving differential equations using the Laplace transform?

A: A differential equation can be solved in the following steps: Take the Laplace Transform of the…

Q: Solve the given symbolic initial value problem. у'+ 9y'+ 20y 3D е ""6(t-3); у(0) 3 2, у'(0)%3 - 9…

A: We have to solve the given differential equations using Laplace transform.

Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

A:

Q: Gニ +3.94 り(s) = \ y(0)= 3.9

A: According to the given information, it is required to solve t he given differential equation using…

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

A:

Q: The charge of the condenser Q(t) = 1(t)dt is the rate of change of the current I. %3D other words, I…

A:

Q: 1. x"(t) – 4x'(t) + 4x(t) = 4e²* ; x(0) = -1, x'(0) = -4 %3D

A:

Q: 6y = -12 y (0) = 1, y' (0) =4. y" (0) = -2 %3D 3.) at + 4 dt

A: Take laplace on both sides of the given equation and then Use-…

Q: According to Kirchoff's voltage law, the sum of the voltage drops across these elements is equal to…

A:

Q: d'y dt² dy dt y (0) = 0 y'(0) = 1 - 3 - + 2y = sin t

A: